These are Questions/answers for #1, 2, 3, 17, 18, 19 & 20 if you can't see what it says in the picture (Please answer all questions in correct order)

#1.Given w = −96i −180j, what are the magnitude and direction of −4w? Round the answers to the nearest whole number.

204; 62°

816; 62°

204; 242°

816; 242°


# 2. A basketball player shoots a free throw, where the position of the ball is modeled by x = (24cos 48°)t and y = 6.1 + (24sin 48°)t − 16t 2. What is the height of the ball, in feet, when it is 13 feet from the free throw line? Round to three decimal places.

10.053

10.292

10.673

11.025


#3.Vectors u and v are shown on the graph.

vectors u and v share an initial point and vector u points down 8 units and vector v points to the right 6 units

Which of the following vectors represents u + v? (Please put/show a graph if you can)


17.What are the magnitude and direction of u + v + w? Round the magnitude to three decimal places and the direction to the nearest degree.

53.241; 355°

52.822; 355°

53.241; 5°

52.822; 5°


#18. Which point represents z1 + z2?

P

Q

R

S


Question 19. A barge is being towed by two tugboats, using ropes with force vectors as shown.

Two vectors named F sub 1 and F sub 2 that share an initial point from the barge each pointing to a different tugboat

Given vector F sub 1 equals open angled bracket 12000 comma 7000 close angled bracket and vector F sub 2 equals open angled bracket 14500 comma negative 5000 close angled bracket comma what is the angle between the ropes? Round to the nearest degree.

31°

33°

49°

54°


Question 20.Given v = 8i − 3j and w = −12i + 4j, find 7v − 2w.

−80i − 29j

−80i + 29j

80i − 29j

80i + 29j

Answer:

See below for answers and explanations (along with a graph for #3)

Step-by-step explanation:

Problem #1

Applying scalar multiplication, [tex]-4w=-4\langle-96,-180\rangle=\langle384,720\rangle[/tex].

Its magnitude would be [tex]||-4w||=\sqrt{384^2+720^2}=816[/tex].

Its direction would be [tex]\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ[/tex].

Thus, B) 816; 62° is the correct answer

Problem #2

Find the time it takes for the ball to cover 13ft:

[tex]x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095[/tex]

Find the height of the ball at the time it takes for the ball to cover 13ft:

[tex]y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053[/tex]

Thus, A) 10.053 is the correct answer

Problem #3

We have [tex]u=\langle0,-8\rangle[/tex] and [tex]v=\langle6,0\rangle[/tex] as our vectors. Thus, [tex]u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle[/tex]. Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.

Problem 4 (#7)

[tex]\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46[/tex]

Thus, C) -46 is the correct answer

Problem 5 (#8)

Find [tex]r[/tex] and [tex]\theta[/tex]:

[tex]r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246[/tex]

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ[/tex]

Find the true direction angle accounting for Quadrant IV:

[tex]\theta=360^\circ-75.964^\circ=284.036^\circ[/tex]

Write the complex number in polar/trigonometric form:

[tex]z=8.246(\cos284.036^\circ+i\sin284.036^\circ)[/tex]

Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer

Problem 6 (#12)

Eliminate the parameter and find the rectangular equation:

[tex]x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0[/tex]

Thus, D) x^2-9y+45=0 is the correct answer

Problem 7 (#13)

Find the magnitude of the vector:

[tex]||v||=\sqrt{(-77)^2+36^2}=85[/tex]

Find the true direction of the vector accounting for Quadrant II:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ[/tex]

Write the vector in trigonometric form:

[tex]w=85\cos155^\circ i+85\sin155^\circ j[/tex]

Thus, D) w=85cos155°i+85sin155°j is the corrwect answer

Problem 8 (#15)

[tex]\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)[/tex]

Thus, C) (-3,-13) is the correct answer

Problem 9 (#16)

Treat the golf ball and wind as vectors:

[tex]u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle[/tex] <-- Golf Ball

[tex]v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle[/tex] <-- Wind

Add the vectors:

[tex]u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{(-0.225)^2+1.755^2}\approx1.769[/tex]

Find the true direction of the resultant vector accounting for Quadrant II:

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{1.755}{-0.225}\biggr)\approx-82.694^\circ\approx-83^\circ=180^\circ-83^\circ=97^\circ[/tex]

Thus, B) 1.769 m/s; 97° is the correct answer

Problem 10 (#17)

Identify the vectors and add them:

[tex]u+v+w=\langle50\cos20^\circ,50\sin20^\circ\rangle+\langle13\cos90^\circ,13\sin90^\circ\rangle+\langle35\cos280^\circ,35\sin280^\circ\rangle=\langle50\cos20^\circ+13\cos90^\circ+35\cos280^\circ,50\sin20^\circ+13\sin90^\circ+35\sin280^\circ\rangle=\langle53.062,-4.367\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241[/tex]

Find the true direction of the resultant vector accounting for Quadrant IV:

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ[/tex]

Thus, A) 53.241, 355° is the correct answer

Problem 11 (#18)

We observe that [tex]z_1=-8-6i[/tex] and [tex]z_2=4-4i[/tex], hence, [tex]z_1+z_2=(-8-6i)+(4-4i)=-4-10i[/tex]

Thus, Q is the correct answer

Problem 12 (#19)

Find the dot product of the vectors:

[tex]F_1\cdot F_2=(12000*14500)+(7000*-5000)=174000000+(-35000000)=139000000[/tex]

Find the magnitude of each vector:

[tex]||F_1||=\sqrt{12000^2+7000^2}=1000\sqrt{193}\\||F_2||=\sqrt{14500^2+(-5000)^2}=500\sqrt{941}[/tex]

Find the angle between the two vectors:

[tex]\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ[/tex]

Thus, C) 49° is the correct answer

Problem 13 (#20)

Using scalar multiplication, [tex]7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j[/tex]

Thus, A) -80i - 29j is the correct answer

Number two and three please asap

CAN SOMEONE PLEASE HELP ME WITH THIS.

I AM A LIL BIT CONFUSED HERE CAN SOMEBODY HELP ME

Pythagorean Theorem

solve for the missing side round to the nearest 10th I will mark you BRAINLIEST IF ANSWEREE CORRECTLY NO LINKS IF YOU DO NOT KNOW THE ANSWER DONT COMMENT ON THIS THREAD

If you need $25,000 eight years from now, what is the minimum amount of money you need to deposit
into a bank account that pays an annual percentage rate (APR) of 5% that is compounded-
a. once a year?
Please Help me on this ! ( don’t send links)

45 miles divided by 1 hour and 45 minutes

The dimensions of a triangular prism are shown in the diagram. The prism is not drawn to scale.
What is the volume of the triangular prism in cubic centimeters?

What is the length of the subtended arc, if the radius is 12 units and the central angle measures 45 degrees? (give the answer in decimal form rounded to the nearest tenth.)​

Help please with this

he price of a laptop was marked 80 percent off because it had a cracked screen.
If this resulted in a savings of $600, what is the value of x in the table above?

Please help me solve this

shift up 5 units

shift down 5 units

shift right 5 units

shift left 5 units

Roderick works as an architectural draftsman for an engineering firm. His monthly salary is $3,204.17. After taxes and other deductions, he takes home $2,317.56. His wife works as an electronics technician and earns $25.07 per hour. She works 37.5 hours each week and is paid every other week.
Based on this information, what is their gross income for six months?

Hey whats 56x78 then divide it by 5.

Dan read 126 pages of his book. He has 68% of his book left to read. How many pages are
in his bool
Enter the number in the box.

If a and b are positive integers the system consists of which inequalities?

10.0% complete
Question
You are writing a book about a 3,030-mile bike race across the United States. You wonder about a title, and how many pedal strokes it takes to finish the race. Assuming a pedal stroke is about 16 feet on average, which of the following would be the best book title?

Help pls I’m literally so confused TvT

Write the number in expanded NOTATION 14.95

simplify 3(6a+3b)+5(2a-b).​

Jack wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 36 feet from the tree, and Tom is standing 9.1 feet from the mirror, as shown in the figure. His eyes are 6 feet above the ground. How tall is the tree? Round your answer to the nearest foot.

Which expression is equivalent to (-3m-2n³)²(4mn²p-4)?

Determine the midpoint of each line segment with the given endpoints.

1. (-2,5) and (0,2)
2. (0,3) and (0,-3)
3. (-2,0) and (-4,0)
4. (9,0) and (0,-7)​

which product is greater than 1/2
5/2x1/2
3/3x1/2
2/3x1/2
4/5x1/2

find the area of the shape below giving your answer to the 1 decimal place. 10cm, 15 cm​

At a fudge shop, they cut a sheet of fudge into one-ounce pieces.
What would happen if they cut the sheet of fudge into one-pound pieces?
A.There would be more pieces.
B. There would be fewer pieces.
C. There would be no pieces.
D. There would be the same number of pieces.

select the correct number from each list to complete the equation.
8
-)+?
8
2
2.
-2
-2
Mit
to it
-4
3
-3
4

Square PQRS is drawn inside rectangle ABCD such that side PQ is on side AB and side SR is on side DC, as shown below. Line segment PB is 17 inches long and line segment DR is 15 inches long. What is the perimeter of rectangle ABCD?

9. You are installing a swimming pool. Write a polynomial that represents the area of the walkway
8 ft width of the pool
(6x-4) ft length (of the pool)
(2x + 6) ft length of the Walk way
10x ft width of the Walk way
​

Which expression is equivalent to 16^3? 2^7 2^11 2^12 2^64